SAT Math · Advanced Math

Function Notation on the Digital SATWhat it tests, how to approach it, and where students get trapped

Evaluating and composing functions written as f(x), interpreting what f(a) = b means, and translating between notation, tables, and graphs.

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Function Notation in Our Question Bank

31

Total questions

15

Easy

8

Medium

8

Hard

These counts cover the full Grind1600 bank. On the Free plan you get the first 5 easy, 5 medium, and 5 hard questions in Advanced Math.

What the SAT Actually Tests

These questions strip functions down to the notation itself: given f(x) = 3x − 7, find f(4); given a table, find f(g(2)); or interpret a statement like f(20) = 12 in a real context. They're among the most learnable questions on the entire Math section.

Read f(input) = output every single time. For composition, work inside-out: evaluate the inner function first, then feed the result to the outer one. For interpretation questions, restate in words — f(20) = 12 means "when the input is 20 units, the output is 12 units" — then match to the choice that says exactly that.

Original Function Notation Practice Questions

These fixed public samples come from Grind1600's original question bank. Choose an answer and check your reasoning before reading the explanation.

Question 1easy
The function g is defined by g(x) = x² - 3. Which of the following is equal to g(5)?
Question 2medium
A theater sold 50 tickets to a show before online ticket sales opened. The function h is defined by h(t) = 50 + 12t, where h(t) is the total number of tickets the theater has sold t hours after online sales opened. Which of the following is the best interpretation of h(3) = 86?

Traps to Avoid

  • Evaluating f(g(x)) outside-in instead of inside-out.
  • Treating f(x + 2) as f(x) + 2 — a horizontal shift is not an output shift.
  • In context questions, swapping which real-world quantity is the input and which is the output.

Want more official questions for this skill?

The College Board Student Question Bank can filter official SAT questions by section, domain, skill, and difficulty. Read our question-bank workflow guide before choosing a set.

More Advanced Math Skills

Equivalent Expressions

Rewriting algebraic expressions — factoring, expanding, combining rational expressions, and applying exponent rules to show two forms are equivalent.

Nonlinear Equations & Systems

Solving quadratic, radical, rational, and exponential equations, plus systems that mix a line with a curve — including discriminant reasoning.

Nonlinear Functions

Quadratic, exponential, and polynomial functions: vertex form, growth and decay, end behavior, and interpreting key features in context.

Continue With Advanced Math Practice

Practice is sorted by domain and difficulty. On the Free plan you get the first 5 questions of each difficulty in Advanced Math. Pro opens every question in the bank.

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Last reviewed August 29, 2026 · Grind1600 Editorial Team